1. Field of the Invention
The present invention relates to compensation of physical layer impairments on communication systems and particularly to a method and apparatus for I/Q mismatch calibration in a receiver.
2. Description of the Prior Art
OFDM is a multi-channel modulation system employing Frequency Division Multiplexing (FDM) of orthogonal sub-carriers, each modulating a low bit-rate digital stream. The simplest way to describe an orthogonal frequency-division multiplexing (OFDM) signal is as a set of closely spaced frequency-division multiplexed carriers. While this is a good starting point for those unfamiliar with the technology, it falls short as a model for analyzing the effects of signal impairment.
The reason it falls short is that the carriers are more than closely spaced; they are heavily overlapped. In a perfect OFDM signal, the orthogonality property prevents interference between overlapping carriers. This is different from the FDM systems. In FDM systems, any overlap in the spectrums of adjacent signals will result in interference. In OFDM systems, the carriers will interfere with each other only if there is a loss of orthogonality. So long as orthogonality can be maintained, the carriers can be heavily overlapped, allowing increased spectral efficiency.
Table 1 lists a variety of common analog signal impairments and their effects on both OFDM signals and the more familiar single-carrier modulations such as quadrature phase-shift keying (QPSK) or 64-QAM (quadrature amplitude modulation). Most of these impairments can occur in either the transmitter or the receiver.
ImpairmentOFDMQPSKI/Q gainState spreadingDistortion ofbalance(uniform/carrier)constellationI/Q quadratureState spreadingDistortion ofskew(uniform/carrier)constellationI/Q channelState spreadingState spreadingmismatch(non-uniform/carrier)UncompensatedState spreadingSpinningfrequency errorconstellationPhase noiseState spreadingConstellation(uniform/carrier)phase arcingNonlinearState spreadingState spreadingdistortionLinearUsually no effectState spreadingdistortion(equalized)if not equalizedCarrierOffset constellationOffsetleakagefor center carrierconstellationonly (if used)FrequencyState spreadingConstellationerrorphase arcingAmplifierRadial constellationRadial constellationdroopdistortiondistortionSpuriousState spreading orState spreading,shifting of affectedgenerally circularsub-carrier
For cost reasons, analog in-phase and quadrature (I/Q) modulators and demodulators are often used in transceivers —especially for wide bandwidth signals. Being analog, these I/Q modulators and demodulators usually have imperfections that result in an imperfect match between the two baseband analog signals, I and Q, which represent the complex carrier. For example, gain mismatch might cause the I signal to be slightly different from the Q. In a single-carrier modulation system, this results in a visible distortion in the constellation—the square constellation of a 64-QAM signal would become rectangular.
To better understand how gain imbalance will affect an OFDM signal, look at the equations describing each individual sub-carrier. In the following analysis, it's important to keep in mind that, while an individual sub-carrier is analyzed, the I/Q gain imbalance error is on the signal that is the composite of all sub-carriers.
In the equation (1), Ck,m is a complex number representing the location of the symbol within the constellation for the kth sub-carrier at the mth symbol time. For example, if sub-carrier k is binary-phase-shift-keying (BPSK) modulated, then Ck,m might take on values of ±1+j0. The complex exponential portion of equation (1) represents the kth sub-carrier, which is amplitude- and phase-modulated by the symbol Ck,m. Therefore:Ck,m(ej2πkΔft)  (1)
Using Euler's relation, the equation (1) can be rewritten as:Ck,m(cos(2π·kΔft)+j sin(2π·kΔft))  (2)
Now add the term “β” to represent gain imbalance. For a perfect signal, set β=0. As shown, the gain imbalance term will also produce a gain change. This was done to simplify the analysis. Therefore:Ck,m((1+β)cos(2π·kΔft)+j sin(2π·kΔft)  (3)
The equation can be rearranged and this can be rewritten as the sum of a perfect signal and an error signal:Ck,m(cos(2π·kΔft)+j sin(2π·kΔft))+Ck,mβ cos(2π·kΔft)  (4)
Finally, converting back into complex exponential notation, we get:
                                          C                          k              ,              m                                ⁢                      ⅇ                          j2π              ⁢                                                          ⁢              k              ⁢                                                          ⁢              Δ              ⁢                                                          ⁢              f              ⁢                                                          ⁢              t                                      +                              (                                          C                                  k                  ,                  m                                            ⁢                              β                2                                      )                    ·                      (                                          ⅇ                                  j2π                  ⁢                                                                          ⁢                  k                  ⁢                                                                          ⁢                  Δ                  ⁢                                                                          ⁢                  f                  ⁢                                                                          ⁢                  t                                            +                              ⅇ                                                      -                    j2π                                    ⁢                                                                          ⁢                  k                  ⁢                                                                          ⁢                  Δ                  ⁢                                                                          ⁢                  f                  ⁢                                                                          ⁢                  t                                                      )                                              (        5        )            
In words, the equation (5) shows that a gain imbalance produces two error terms. The first error term is at the frequency of the kth sub-carrier. The second error term is at the frequency of the −kth sub-carrier. The phase and magnitude of the error terms are proportional to the symbol being transmitted on the kth sub-carrier. Another way of saying this is that I/Q gain imbalance will result in each sub-carrier being interfered with by its frequency mirror-image sub-carrier. Persons skilled in the art will instantly recognize this as imperfect sideband cancellation.
The equation (5) has several implications. First, it is generally true that for sub-carriers used to carry data (as opposed to pilots), the symbol being transmitted at any given time on the kth sub-carrier is uncorrelated to the symbol on the −kth sub-carrier.
For a given sub-carrier, the lack of correlation from the mirror-image sub-carrier implies a certain randomness to the error. This results in a spreading of the sub-carrier's constellation states in a noise-like fashion. This is especially true for higher-order modulations such as 64-QAM. For lower-order modulations, such as BPSK, the error term from the mirror-image carrier has fewer states.
This can result in constellations where the BPSK pilot carriers of an 802.11a signal exhibit spreading that does not appear noise-like. Also, as the BPSK pilots do not have an imaginary component; the error terms associated with the pilot sub-carriers are real—so the spreading is only along the real (I) axis. Note that the phase relationships between the pilot carriers in an 802.11a system are highly correlated, so the errors introduced by quadrature errors are not random.
Quadrature skew produces error terms similar to those produced by gain imbalance. Quadrature skew occurs when the two oscillators used in an I/Q modulator or demodulator do not differ by exactly 90°. For a small angular error, it can be shown that the resulting error is orthogonal to the data. This is indicated by the j in front of the error terms in the equation (6). As with gain imbalance, the error generates energy at the kth and −kth sub-carriers. Again, the 802.11a BPSK pilots do not have an imaginary component, so the error term, which is now orthogonal, causes spreading along the Q axis. For the QPSK carriers in this example, the error is also orthogonal. However, unlike BPSK, a QPSK constellation doesn't look any different when rotated by 90°. (See the equation (6).):
                                          C                          k              ,              m                                ⁢                      ⅇ                          j2π              ⁢                                                          ⁢              k              ⁢                                                          ⁢              Δ              ⁢                                                          ⁢              f              ⁢                                                          ⁢              t                                      +                  j          ⁢                                          ⁢                                                                      C                                      k                    ,                    m                                                  ⁢                ϕ                            2                        ·                          (                                                ⅇ                                      j2π                    ⁢                                                                                  ⁢                    k                    ⁢                                                                                  ⁢                    Δ                    ⁢                                                                                  ⁢                    f                    ⁢                                                                                  ⁢                    t                                                  +                                  ⅇ                                                            -                      j2π                                        ⁢                                                                                  ⁢                    k                    ⁢                                                                                  ⁢                    Δ                    ⁢                                                                                  ⁢                    f                    ⁢                                                                                  ⁢                    t                                                              )                                                          (        6        )            
In both 802.11a and Hiperlan2, a channel estimation sequence is transmitted at the beginning of a burst. This special sequence is used to train the receiver's equalizer. The intended function of the equalizer is to compensate the received signal for multi-path distortion—a linear impairment in the signal that is the result of multiple signal paths between the transmitter and the receiver. As the ideal channel estimation sequence is known by the receiver, the receiver can observe the effects of the channel on the transmitted signal and compute a set of equalizer coefficients.
In the transmitter, the channel estimation sequence is created by BPSK modulating all 52 carriers for a portion of the preamble. Not coincidentally, the equalizer consists of 52 complex coefficients—one for each sub-carrier. It should come as no surprise that each sub-carrier in the channel estimation sequence has the greatest influence on the equalizer coefficient computed for that same sub-carrier.
The channel estimation sequence, and the receiver algorithms that compute the equalizer coefficients, are not immune from signal impairments. Consider, for example, the effect of I/Q gain imbalance on sub-carriers +26 and −26 of the channel estimation sequence. Recall from equation (5) that each sub-carrier has two error terms: one at the same frequency as the sub-carrier, and one at the mirror image frequency. The I/Q gain imbalance will cause mutual interference between sub-carriers +26 and −26.
From the IEEE 802.11a standard, the sub-carrier modulation for the channel estimation sequence is defined to be C−26=1+j0 and C+26=1+j0. Using these values in equation (5), one can easily determine that the two sub-carriers, when combined with the resulting error terms, will suffer an increase in amplitude. The equalizer algorithm will be unable to differentiate the error from the actual channel response, and will interpret this as a channel with too much gain at these two sub-carrier frequencies. The equalizer will incorrectly attempt to compensate by reducing the gain on these sub-carriers for subsequent data symbols.
The result will be different for other sub-carrier pairs, depending on the BPSK channel estimation symbols assigned to each.
With QPSK sub-carriers, the equalizer error caused by gain imbalance, or quadrature skew, results in seven groupings in each corner. Each QPSK sub-carrier suffers from QPSK interference from its mirror image. This results in a spreading to four constellation points in each corner. Each QPSK sub-carrier also suffers from a bi-level gain error introduced by the equalizer. This would produce eight groupings, except that the gain error is such that corners of the groupings overlap at the ideal corner state. Only seven groupings are visible.
I/Q Channel Mismatch
When the frequency response of the baseband I and Q channel signal paths are different, an I/Q channel mismatch exists. I/Q channel mismatch can be modeled as a sub-carrier-dependent gain imbalance and quadrature skew. I/Q gain imbalance and quadrature skew, as described above, are simply a degenerate form of I/Q channel mismatch in which the mismatch is constant over all sub-carriers. Think of channel mismatch as gain imbalance and quadrature skew as a function of a sub-carrier. It is still generally true that channel mismatch causes interaction between the kth and −kth sub-carriers, but that the magnitude of the impairment could differ between the kth and the (k+n)th carriers.
Delay mismatch is a distinct error. It can occur when the signal path for the I signal differs in electrical length from the Q signal. This can be caused by different cable lengths (or traces), timing skew between D/A converters used to generate the I and Q signals, or group delay differences in filters in the I and Q signal paths.
What makes this error distinctive is that the error is greater for the outer carriers than it is for the inner carriers. In other words, the error increases with distance from the center sub-carrier. With a vector spectrum display, it may be shown that the signal error is a function of the sub-carrier number (frequency). That is to say, the phase arcing may occur as a function of frequency.
In order to eliminate the effects of the previously described impairments on the OFDM systems, various kinds of compensation circuits and methods have been proposed.
FIG. 1 shows the quadrature gain and phase imbalance correction circuitry of a receiver disclosed in U.S. Patent Application No. 285151. FIG. 1 illustrates a communications device 110 suitable for receiving and correcting I and Q (In phase and Quadrature phase) signals. There are two essential parts to the device 110, the path of the received signals and the signal path of the signals used to mix with the received signals. The received signal path includes a low noise amplifier 111, two mixers 112 and 113, two coupling capacitors 114 and 115 and two filters 116 and 117. Finally the signal path contains gain amplifiers 118 and 119 before the received signal is input into A/D converters 120 and 121 for processing by the digital signal processor 122. The mixing signals are produced using local oscillators 123 and 124, a phase locked loop 125, a filter 126, a phase shifter 127 and a mixer 128.
In the received signal path, the LNA (111) is a standard low noise amplifier commonly used to amplify low power high frequency RF signals. The incoming radio signal LNA comes from an antenna (not shown). The received signal will be broken into quadrature components by using mixing circuits M1 (112) and M2 (113) and phase adjusting circuit P1 (129). The outputs of M1 and M2 will become the baseband signals. For example, if the incoming signal has a bandwidth of 20 MHz, each of the I and Q branches will be signals of 10 MHz bandwidth respectively. As is conventional in quadrature circuits, capacitors C1 and C2 (114 and 115) are used to block any DC components of the received signal and filters F1 and F2 (116 and 117) are used to further filter unwanted signals. Before any I/Q modulation is performed however, it is critical that the receiver be properly calibrated.
In order to produce a reliable calibration tone in the mixing signal path, the local oscillator L1 (123) is mixed with a low frequency tone produced by L2 (124). An example of these frequencies would be L1 set at 5 Gigahertz, while L2 is set at 5 Megahertz. The local oscillator L1 is also used with a Phase Locked Loop PLL (125) and a filter F3 (126). These two signals are multiplied by a mixing circuit M4 (128). The resulting multiplication of two sine waves of differing frequencies results in two signals being produced, wherein the resulting sine wave are at different frequencies. Therefore the mixer M4 produces two signals for the calibration process.
The two calibration tones will be fed into Mixers M1 and M2 for quadrature processing. The In-phase branch would be a clear signal but the Quadrature phase would be zero. In order to overcome this problem, a Phase Shifter P2 is implemented. The phase shifter P2 adds an angle theta to the frequency of a calibration tone signal. For example, when P2 is set to zero, VI(t) is cos (wt) and VQ(t) is zero. When P2 is set to 90 degrees, the VI(t) signal is nonexistent while VQ(t) is cos (wt).
The calibration process using Phase Shifter P2 (127) would then be as follows. P2 is adjusted so as to obtain the maximum value of signal in the VI(t) branch. The adjustment of P2 is performed by the Digital Signal Processing chip (122). The maximum signal level is measured by baseband processor chip 122 and stored. Then P2 is adjusted by 90 degrees until the signal in the Q branch is at a maximum level. The maximum level of the Q branch is also measured and stored in the baseband processor chip 122. Once these maximum values of each branch are known, the baseband processor chip may perform a gain imbalance calibration. This gain imbalance correction may be performed by amplifiers G1 and G2 (118 and 119) or after analogue to digital signal conversion (A/D) in the baseband processor chip 122. It is noted that G1 and G2 may perform the gain adjustments for the receiver as a whole. It is also noted that G1 and G2 are controlled together as opposed to separately. The I and Q gains are therefore made equal to avoid any sideband production and distortion of the desired signal. The present invention also allows for gain imbalance calibration to be performed at any level of gain as set by G1 and G2.
With respect to the IQ phase error calibration, P2 would be set at an angle such as 45 degrees. This ensures a signal of almost equal value in both the I and Q branches. By simply multiplying the two signals one can detect the relative phase of the I and Q branches. The product of a sine and cosine signal should result in zero. Mixer circuit M3 (31) accomplishes the multiplication of the I and Q signals and outputs a signal to the filter F4 (30). If this is not the case, meaning that the I and Q branches are not exactly 90 degrees out of phase as desired, a phase error signal is produced. This signal is fed back through an amplifier and filter EF to Phase Shifter P1 to compensate for the error. Ideally the phase difference between the I and Q branches should be 90 degrees. Therefore, the adjustment of P2 with the appropriate gain control in addition with the adjustment of P1, allow for an optimum phase imbalance to be achieved. It is noted that P1 may be in the RF path instead of being in the local oscillator path if desired.
U.S. Pat. No. 6,122,325 also discloses a method for detecting and correcting in-phase/quadrature imbalance in digital communication receivers. The method includes the steps of assuming that a signal imbalance exists in the received signal, the signal imbalance having an amplitude imbalance and a phase imbalance, generating an amplitude imbalance correction factor and a phase imbalance correction factor to lessen the signal imbalance, and re-evaluating the amplitude and phase imbalance correction factors over a set of readings of the in-phase and quadrature components until the signal imbalance is minimized.
U.S. Pat. No. 5,949,821 discloses an apparatus for correcting phase and gain imbalance between in-phase and quadrature components of a received signal based on a determination of peak amplitudes. As shown in FIG. 2, it includes an equalizer 226 for correcting imbalance between in-phase and quadrature components of a received signal. The equalizer 226 determines peak amplitude for the in-phase and quadrature components, and the phase imbalance between both components. At least one of the in-phase and quadrature components is adjusted based on a function of the phase imbalance, and of the ratio of peak amplitudes of the in-phase and quadrature components.
Although there are already many kinds of compensation circuits and methods, it is still a goal of research to propose newer and better solutions to the I/Q mismatch problem in OFDM systems.